JOURNAL OF SOUND AND VIBRATION Journal of Sound and Vibration 303 (2007) 343–356 Geometrical design method of multi-degree-of-freedom dynamic vibration absorbers Seon J. Jang, Yong J. Choi à School of Mechanical Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, Seoul 120-749, Republic of Korea Received 23 May 2006; received in revised form 25 October 2006; accepted 19 January 2007 Available online 21 March 2007 Abstract This paper presents a new geometrical design method of multi-degree-of-freedom (mdof) dynamic vibration absorbers that reduce multiple modes of vibration. The design of an mdof vibration absorber involves, in general, the complexity of the equations and large numbers of design variables. For this reason, previous researches mainly focused on finding optimized stiffness and damping values that minimize the vibration responses. In this paper, we introduce a simple geometrical design method in which the sets of three mutually orthogonal line springs are used to first simplify the stiffness matrix. The dynamic equations of a main body and an absorber are then decoupled to obtain the geometric design rules for an mdof absorber. Numerical examples are used to illustrate the new design method. r 2007 Elsevier Ltd. All rights reserved. 1. Introduction A typical dynamic vibration absorber has a single degree-of-freedom (dof). It has a tuned spring and mass arranged in the direction of the excitation force. However, many practical vibration systems are regarded as mdof vibration systems that have multiple vibration modes and resonant frequencies. In order to deal with multiple vibration modes, some research works have been focused on the use of a single vibration absorber or a set of single dof vibration absorbers. Vakakis and Paipetis [1] investigated the effect of a single dof vibration absorber mounted on an mdof system. Sadek [2] estimated the optimal stiffness and damping constants of multiple single dof vibration absorbers attached to an mdof system. A single rigid body suspended by springs has 6dof in space. This implies that a single rigid body can be used as a 6dof vibration absorber. In light of this nature, Zuo and Nayfeh [3] showed a single body vibration absorber, which can diminish multiple vibration modes. They regarded this as an optimization problem solving for optimal spring and damping constants set up in the estimated positions and directions. The design of an mdof vibration absorber using a single body can be greatly simplified when an adequate geometrical approach to the design is taken. To make use of every dof of the vibration absorber, the dynamic equation of the vibration absorber is completely decoupled. By describing stiffness matrix and mass matrix via screw theory [4], one can easily obtain decoupling conditions of the dynamic equation. From the decoupled ARTICLE IN PRESS www.elsevier.com/locate/jsvi 0022-460X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsv.2007.01.017 à Corresponding author. +82 2 2123 2826; fax: +82 2 362 2736. E-mail address: yjchoi@yonsei.ac.kr (Y.J. Choi).